Problem: Simplify the following expression: $n = \dfrac{-10t^2 + 40t + 50}{t - 5} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ n =\dfrac{-10(t^2 - 4t - 5)}{t - 5} $ Then we factor the remaining polynomial: $t^2 {-4}t {-5} $ ${-5} + {1} = {-4}$ ${-5} \times {1} = {-5}$ $ (t {-5}) (t + {1}) $ This gives us a factored expression: $\dfrac{-10(t {-5}) (t + {1})}{t - 5}$ We can divide the numerator and denominator by $(t + 5)$ on condition that $t \neq 5$ Therefore $n = -10(t + 1); t \neq 5$